Response to "Comment on 'Higher order reentrant post modes in cylindrical cavities'" [J. Appl. Phys. 123, 226101 (2018)]

We recently rigorously described using finite element analysis a cylindrical cavity resonator, with a cylindrical post inserted along the central axis. Such a cavity has a well known reentrant mode where an E-z field exists in the gap between the lid and the post. In McAllister et al., J. App. Phys. 122, 144501 (2017), we rigorously analysed higher order modes with similar characteristics to the well known reentrant mode, which we dubbed "higher order re-entrant post modes." The author claims in S. Belomestnykh, J. Appl. Phys. 123, 226101 (2018) that these modes have been described before as foreshortened quarter-wave resonators. We discuss the differences between the results of rigorous finite element modelling and the model proposed in the comment and show that the proposed description is a crude non-Maxwellian model, only approximately valid in a finite region of the cavity tuning range with on average similar to 9.6% agreement with experimental frequencies for the first higher order mode. The model assumes simple electromagnetic field patterns which do not satisfy Maxwell's equations, and we show that they vary significantly from the rigorous analysis based on Maxwell's equations. The foreshortened quarter-wave resonator model cannot be used to accurately calculate geometry factors or other factors that require precise knowledge of the fields, such as those computed in the design of cavities for axion experiments. We conclude that the reentrant mode description in the paper is favourable. Published by AIP Publishing.